I have no precise, scientific answers to give you regarding 'magic.' Despite centuries of detailed experimentation by local Unicorns, there is no neat system that fully and reliably explains its nature, structure, or behaviour. It is a force that does not appear to be generated from any mundane energy, process or material we Humans are familiar with. It reacts to and can affect in turn almost every known aspect of the universe, and possibly more.
But when regarding magic, what you need to be aware of is how it can change things from what you expect to what should not be possible. The strangeness here is in the exceptions, rather then manifesting as a new set of rules. Things here still fall down, not sideways. Fire is hot, water is wet.
As an example, gravity works exactly as it should. The Unicorns have astrological models of their solar system and the bodies that move in it. They understand that their world turns as it orbits the sun, and that Celestia and Luna can control the cycles of day and night. Physics ensures the former, and magic allows the latter. These facts do not conflict.
I suggest you just don't think too hard about it.
It's not something you generally have to worry about anyways. Magic mainly works 'in the background' by subtly tweaking forces beyond your perception. For example, the monsters created in the depths of the Everfree Forest are still organic creatures that can be dissected and analyzed. In the end, while their shapes and abilities may be improbable, they are never outright impossible. Magic bends the rules, and a lot of magic can stretch the rules pretty far, but that does not mean that magic has no rules of its own.
Speaking for day-to-day life, you've seen that magic lends a certain static quality to the landscape. The world changes slowly, depending on the actions of its inhabitants to kick-start certain processes.
Earth Ponies have a facility with all things related to the Earth, and to a lesser degree, any solid matter. Where they work, plants grow and bear fruit. Stone crumbles easily where they mine, and holds solid where they build.
The Pegasus Ponies are aligned with the sky and its energies. Magic allow them to fly despite their bodies' imbalanced equations of weight, air displacement, and aerodynamics. Their passage stirs the air and directs the weather. They walk on and sculpt clouds.
Unicorns are unique among ponies for their huge variety of possible magical affinities, whereas the specialities of individual Earth and Pegasus Ponies fall somewhere within broad but well-defined fields. Unicorns 'spells' are simply repeatable ways of pushing magic in a certain way to get a certain result. Creating reliable spells that can be taught to others is a long and gruelling process of experimentation, which does not require, but is made easier by, an understanding of mundane science.
Spellcasting is not a discipline limited to Unicorns. Earth Ponies can learn to 'hold' tools with telekinetic force or even cause small cracks and breaks to form or mend through sheer willpower. A simple extension of Pegasus flight-magic allows them to create gusts of wind with a wave of their wings, or leave a contrail of storm clouds in their wake. It is very difficult, comparable to a human taking control of an unconscious process like digestion, breathing, or heartrate. Most prefer to refine a few simple spells to perfection, as while a talented Pony can perform a wide array of effects, magic is an intrinsic part of one's nature, and trying to push it too far in different directions can have strange side-effects upon a Pony.
Dragons and other races have their own innate abilities and views of magic. Some pursue paths resembling alchemy or shamanism, building systems of magic and training each generation to refine their abilities.
Of course, this is all secondary to the one question you've probably asked every Unicorn that crossed your path, haven't you?
Can a human use magic?
The short answer is 'yes.'
The long answer is 'probably not without going insane in the process.'
Maybe you're seeking magic out of pure childish wonder. Maybe you see it as the answer to all your problems. It's 'awesome' or 'cool' or just a substitute for technology.
But few people handle power well. When someone is stronger, or smarter, or acquires some form of power or influence to lord over others, the effects on their personality is profound. When they use this power to (mis)handle situations, sacrificing morality to receive instant gratification, their success only proves to them that this was the 'right' thing to do. The cycle continues, feeding upon itself.
When magic is involved, the effect is greatly magnified.
Magic shapes and is shaped by a person's nature and unconscious desires. A person that uses magic carefully and for the right reasons stays healthy and sane. A person who does not…does not stay healthy and sane.
Saints, Taoist Immortals, wizards…in various mythologies, it was the work of a lifetime, or even several, to acquire supernatural power. Here, it is handed to you on a silver platter.
If you immediately retort that you could handle this power responsibly, then you need to take a long, hard look at yourself.
As such, humans that develop magical powers while in Equestria have three choices:
1 – Wear a dampening collar to suppress your powers.
2 – Study under a (untranslatable – Priest?) of the philosophy of Harmony, until such time as you are deemed wise and responsible enough to wield these powers.
3 – Refuse seclusion or suppression, try to hide your powers or run away, and if you are found to have harmed anyone, be prepared to be hunted and possibly put down like a rabid animal to prevent your inevitable downward spiral and transformation into a monster.
It may seem harsh, but the alternative is unacceptable.
This section concludes the introduction to living in Equestria. Consult your local library for any more detailed information you may be curious about.
Play nice, stay safe, and have a wonderful time while you're here.